Solve for $x$ and $y$ using elimination. $\begin{align*}-6x-3y &= -3 \\ 5x+5y &= 9\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $5$ and the bottom equation by $3$ $\begin{align*}-30x-15y &= -15\\ 15x+15y &= 27\end{align*}$ Add the top and bottom equations. $-15x = 12$ Divide both sides by $-15$ and reduce as necessary. $x = -\dfrac{4}{5}$ Substitute $-\dfrac{4}{5}$ for $x$ in the top equation. $-6( -\dfrac{4}{5})-3y = -3$ $\dfrac{24}{5}-3y = -3$ $-3y = -\dfrac{39}{5}$ $y = \dfrac{13}{5}$ The solution is $\enspace x = -\dfrac{4}{5}, \enspace y = \dfrac{13}{5}$.